Is it possible to make a script that will run a search every time I search for something in a specific website?

Maybe an odd question, but useful if the answer is yes.

I spend many hours a day searching for Land Records on a specific website. When I find them, I download them into a local folder on my Mac. I have hundreds, maybe thousands of documents, so it's time consuming to do a local search for every document to see if I have it before I do a website search.

So, my question:

Can I make a script that will run every time I click the "search" button on the website?

Order of actions:

1) I Go to website.com

2) I type the document name into search box

3) I click "Search"

4) Upon clicking "Search", apple script will automatically RUN

~Script will take the document name from the search box and run a search in my local folder for any document with the same name.

~If said document is found by script in my local folder, a Finder window will open to location of said document with said document highlighted.

~If said document is not found by script in my local folder, a message will appear that says "Document not found", in which case I will download it from the website.

Thanks in advance for the help that will come from the many great minds that solve these problems in the great Apple Community!